1. Field of the Invention
This invention relates to interferometric methods and systems, and more particularly relates to interferometric methods and systems which use low coherence illumination. Specifically, a preferred embodiment of the invention relates to an interferometric system and method in which both a phase shifting interferometry (PSI) analysis and a scanning white light interferometry (SWLI) analysis are applied to a single 3D interferogram (that is, an interferogram which is comprised of an ensemble of camera frames of interference data, as opposed to a 2D interferogram which is comprised of only a single camera frame of interference data) generated using a low coherence illumination source. Another preferred embodiment of the invention relates to an improved system and method for detecting the position of a contrast peak in a 3D interferogram generated using a low coherence illumination source. Finally, another preferred embodiment of the invention relates to a system and method in which a PSI analysis is applied to a broad-band 3D interferogram generated using a low coherence illumination source.
2. Description of the Related Art
Phase shifting interferometry (PSI) is often used for surface profilometry. A primary advantage of PSI is that it is highly precise; the vertical height precision for PSI is a fraction (e.g., 1/100) of the optical wavelength used to conduct the measurement. This precision is achieved because of the principle behind PSI, which is to determine height differences by first determining a phase difference between light received at first and second pixels of an imaging device (corresponding to first and second locations on the test surface), and then using the phase difference to calculate a height difference. A second advantage of PSI is that it has good vibration immunity characteristics because phase data is acquired for all pixels simultaneously and because the data acquisition time is relatively short.
Generally speaking, however, conventional PSI approaches have been subject to at least two major limitations. First, conventional PSI approaches can only profile smooth surfaces. This is because PSI has the well known phase ambiguity constraint that the maximum physical departure between adjacent measurement sites be less than 1/4 of the optical wavelength. Stated another way, the maximum phase difference between the reference and test light beams must have an absolute value which is less than .pi.. This constraint arises because the arctangent function, which is used to convert phase to distance, is only unique within the range .+-..pi.. This limits the maximum allowable phase difference between the test and reference light beams. Thus, although the use of phase measurements advantageously allows very high precision to be obtained, it disadvantageously limits the maximum physical departure between adjacent measurement sites to 1/4 of the optical wavelength.
Because of the phase constraint, scanning white light interferometry (SWLI) is increasingly being used for surface profilometry. Unlike PSI, which uses a narrow-band source (e.g., a laser source) in order to continuously provide high-contrast interference fringes across the entire surface to be profiled, SWLI uses a broad-band source (e.g., filtered white light) to eliminate the PSI phase constraint. In SWLI, the interference pattern which is generated by the broad-band light source contains regions of high contrast for each location on the test surface. The temporal characteristics of a region of high contrast for a given pixel indicates the height of the corresponding location on the test surface. Therefore, by comparing the temporal characteristics of these regions of high contrast (e.g., when the peak of each high contrast region occurs), a difference in height between two locations can be determined.
The advantage of SWLI is that the maximum physical departure between adjacent measurement sites may be larger than with PSI. Unlike PSI, certain SWLI analysis types do not calculate height differences based on phase differences, and therefore the PSI phase constraint does not apply (i.e., SWLI measurements do not exhibit a 2.pi. phase ambiguity). However, because phase information is not used, certain SWLI analysis types have significantly lower precision than PSI.
Numerous attempts have been made at providing an approach which enjoys the advantages of both PSI and SWLI without suffering any of the disadvantages of either approach. For example, according to one approach, a SWLI measurement is made to produce a first three-dimensional (SWLI) interferogram. Then, the test set-up is changed as needed and, in particular, the light source is changed from a broad-band light source to a narrow band light source. Then, a PSI measurement is made to produce a second three-dimensional (PSI) interferogram. Next, the information obtained from the two separate interferograms (SWLI and PSI) is combined to obtain the surface topography.
This approach, however, suffers its own disadvantages. First, the different spectral and acquisition requirements of the SWLI and PSI measurements requires the interferometer to be able to generate both broad-band and narrow-band illumination and to be able to perform two different types of acquisitions (SWLI and PSI). This increases system cost. Additionally, the fact that two separate measurements are made (including equipment changes) causes measurement time to increase and thereby causes throughput to decrease. Moreover, the delay between the two acquisitions increases susceptibility to errors arising from vibrations, shifts in test surface position, and other error sources.
According to another approach, a SWLI acquisition is performed and a frequency domain analysis (FDA), for example a Fourier analysis, is performed on data generated by the SWLI acquisition. The frequency domain analysis extracts phase information from the SWLI data to improve the precision of the SWLI measurement. The advantage of this approach is that it has nearly the precision of PSI but without the 2.pi. phase ambiguity constraint. The disadvantage of this approach is that, for those features which are vertically separated, it suffers reduced immunity to vibrations as compared to conventional PSI approaches, because the interference data is acquired at different times during different portions of the SWLI scan. Therefore, external vibrations and other detrimental events occurring in the interim can corrupt the measurement.
Ultimately, the precision with which SWLI measurements can be performed is governed by the precision with which contrast peak detection can occur. Prior art peak detection methods have been characterized by curve fitting approaches which rely heavily on ad-hoc assumptions, and which are therefore not particularly accurate. Therefore, in an approach which combines the advantages of PSI and SWLI without any of the associated disadvantages, it would be advantageous if such an approach could also incorporate a more accurate contrast peak detection process. Indeed, since a more accurate contrast peak detection process could generally be used in any SWLI-type approach, such a process would be quite valuable above and beyond the context of a combined SWLI and PSI approach.
A second major limitation of conventional PSI approaches is that they cannot be used in conjunction with a short coherence length illumination source. (Herein, the terms "short coherence length illumination" and "low coherence illumination" are used interchangeably, as are the terms "long coherence length illumination" and "high coherence illumination".) Since short coherence length illumination sources are used for performing SWLI measurements, it would be advantageous if short coherence length illumination sources could also be used for performing PSI measurements, since this would enable the provision of a single interferometric instrument which can perform both types of measurements without significant hardware changes. The reason for the difficulty which has been encountered in attempting to perform PSI measurements using a short coherence length illumination source is as follows. Conventional PSI measures differences in height by measuring differences in phase. During this process, the phase calculations are performed using data which is simultaneously acquired across the entire test surface. In other words, for example, data taken from the same sequence of five scan positions is used in phase calculations for all pixels. If non-simultaneously acquired data is used, then part of the phase difference between two locations will be attributable to the fact that the two locations are at different vertical heights, but part of the phase difference also will be attributable to the scanning of the interferometer. Therefore, in order to address this problem, simultaneously acquired data is utilized.
However, the requirement for acquiring data simultaneously forces the use of long coherence length illumination sources. If a short coherence length illumination source is used, then there is typically not a series of scan positions during which high contrast interference is available across the entire surface. Therefore, data cannot be simultaneously acquired across the entire surface, as is required.
A high coherence illumination source produces high contrast interference throughout a much larger range of scan positions as compared to a low coherence source, thereby making it possible to acquire data simultaneously acquired across the entire surface.